Solving Robin problems in bounded doubly connected regions via an integral equation with the generalized Neumann kernel

Abstract

Abstract. This paper presents a new boundary integral equation method for the solution of Robin problems in bounded doubly connected regions. We show how to reformulate the Robin problems as a Riemann-Hilbert problem which leads to systems of integral equations. Related differential equations are also constructed that give rise to unique solutions. Numerical results on several test regions are presented to illustrate the solution technique for the Robin problems when the boundaries are sufficiently smooth.

Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel

“…In this paper, the integral equation is discretized by the Nystrom method NM with the Trapezoidal rule TR and the Wittich's method WM in [15][16], however in this study the differential equation is discretized in [19]. In conclusion, the presented numerical results clarify that our method can be used to make approximations [20] of good accuracy and best results.…”

“…Are unknown functions in H [15][16].Then the equation (5) can be written briefly describe as equation (5) where…”

“…At recent days, the interplay of RHP and integral equation with the generalized Neumann kernel GNK has been investigated in [14] for simply connected regions with smooth boundaries and in [15][16] for bounded and unbounded doubly connected and multiply connected regions.…”